Population Dynamic Models Generating the Lognormal Species Abundance Distribution

This paper deals with a new class of stochastic species abundance models where the abundances are the points of an inhomogeneous Poisson process. These models are the result of a dynamic approach in which the changes in abundances through time are described by a multivariate diffusion and speciation constitutes a homogeneous Poisson process. In particular, the lognormal model is generated by assuming that the density regulation within each species is given by the Gompertz curve and that the environmental variances are constant. A substantial generalization is obtained by introducing a general type of interspecific density regulation and correlated environmental noise. This more general mechanism also generates the lognormal species abundance distribution.